It's when you're uncomfortable with your penis - its size (too small or too big), it's shape or maybe even its smell.
Gary was in his underwear and felt 'cock conscious'. Tom was swimming in his speedos when a female lifeguard started to talk him, he felt embarrassed and 'cock conscious'.
Paying extra attention to the penis. Typically during sex. Having knowledge of the penis and focusing entirely on its satisfaction.
"Man, Sally is a great fuck. The bitch is really cock conscious, and puts in the effort"